MCMC methods for inference in a mathematical model of pulmonary circulation

Paun, L. M., Qureshi, M. U., Colebank, M., Hill, N. A. , Olufsen, M. S., Haider, M. A. and Husmeier, D. (2018) MCMC methods for inference in a mathematical model of pulmonary circulation. Statistica Neerlandica, (doi:10.1111/stan.12132) (Early Online Publication)

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Abstract

This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics under normal physiological and pathological conditions. This is of medical interest as it enables tracking the progression of pulmonary hypertension. We show how we make the fluids model tractable by reducing the parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive Metropolis algorithm, coupled with constraint non‐linear optimization, is successfully used to learn the parameter values and quantify the uncertainty in the parameter estimates. To accommodate for different magnitudes of the parameter values, we introduce an improved parameter scaling technique in the Delayed Rejection Adaptive Metropolis algorithm. Formal convergence diagnostics are employed to check for convergence of the Markov chains. Additionally, we perform model selection using different information criteria, including Watanabe Akaike Information Criteria.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Paun, Miss Luiza Mihaela and Hill, Professor Nicholas and Qureshi, Mr Muhammad Umar and Husmeier, Professor Dirk
Authors: Paun, L. M., Qureshi, M. U., Colebank, M., Hill, N. A., Olufsen, M. S., Haider, M. A., and Husmeier, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics
College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Statistica Neerlandica
Publisher:Wiley
ISSN:0039-0402
ISSN (Online):1467-9574
Published Online:20 April 2018
Copyright Holders:Copyright © 2018 The Authors, Statistica Neerlandica and VVS
First Published:First published in Statistica Neerlandica 2018
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
694461EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancerRaymond OgdenEngineering and Physical Sciences Research Council (EPSRC)EP/N014642/1M&S - MATHEMATICS